Stochastic single-machine scheduling with random resource arrival times

  • Lianmin Zhang
  • Yizhong Lin
  • Yujie Xiao
  • Xiaopeng Zhang
Original Article


Scheduling in an uncertain environment remains a meaningful yet challenging direction of research. In this paper, we consider a new scheduling setting from practical complex business applications, where resources (e.g., raw materials) used for processing jobs arrive randomly, due to reasons such as unstable transportation service caused by extreme weather conditions, unreliable suppliers, unpredictable industrial actions, etc. Further, jobs must be processed one by one and preemption is not allowed. The processing times of jobs are not known but their distribution. We incorporate these factors into a stochastic single-machine scheduling model and examine two different common types of objectives: minimizing total expected weighted completion time and minimizing total expected weighted squared completion time. We derive and prove a natural and intuitive optimal policy for the model with the first objective. Besides, we find that, under some mild conditions, the well-known policy in stochastic scheduling, WSEPT (weighted shortest expected processing time), still holds optimal for achieving either of objectives. The numerical example further supports and illustrates our results, which provide decision-makers insights into tricky uncertain scheduling problems.


Stochastic scheduling Completion times Squared completion time 



This work was partially supported by the National Natural Science Foundation of China (Grant No. 71501093, 71501090), the Basic Research Foundation (Natural Science) of Jiangsu Province (Grant No. BK20150566).


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Lianmin Zhang
    • 1
  • Yizhong Lin
    • 2
  • Yujie Xiao
    • 3
  • Xiaopeng Zhang
    • 4
  1. 1.School of Management and EngineeringNanjing universityNanjingChina
  2. 2.School of BusinessJiaxing UniversityJiaxingChina
  3. 3.Jiangsu Key Laboratory of Modern LogisticsSchool of Marketing and Logistic Management, Nanjing University of Finance and EconomicsNanjingChina
  4. 4.School of Business AdministrationZhejiang Gongshang UniversityHangzhouChina

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